Design and seismic performance analysis of a novel special-shaped steel tube concrete column steel beam joint

Abstract

In this study, a novel special-shaped steel tube concrete column steel beam joint is proposed. Bolt connections are used to connect the pre-welded steel beam and the special-shaped steel tube concrete column. Based on the finite element software ABAQUS, we established finite element models of the column-beam joints, and conducted a series of finite element analyses to investigate the influence of various parameters on the seismic performance of the joint. These parameters include the shape and size of the flange hole, the shape and size of the web hole, and thickness of the spliced plate on the flange. The results show that the difference between the finite element analysis and experimental results for bearing capacity and displacement is within 10%. This indicates that finite element analysis can be effectively utilized to study the seismic performance of the joint. Compared to joints with non-spliced beam, the rotational deformation capacity of the joint is reduced when using bolts and spliced plates designed by the equal-strength method. The energy dissipation capacity and ductility deformation capacity of the joints with spliced beams are significantly improved by using elliptical bolt holes in the flange, and plastic hinges are formed in the spliced region. The elliptical holes in the web with varying sizes have little effect on the seismic performance of the joint. The thicknesses of the spliced plate ranging from 6 mm to 8 mm has little effect on the seismic performance of the joint, and a thin spliced plate will reduce the seismic performance of the joint. The study presented in this paper can provide a reference for promoting the engineering application of special-shaped steel tube concrete structures.

Keywords

special-shaped steel tube concrete column-beam joint seismic performance finite element analysis bolt connection

Introduction

The concrete-filled steel tube structure has the advantages of high bearing capacity, good seismic performance, good fire resistance, and convenient construction, and has been widely used in high-rise and super high-rise buildings. As a key part of the concrete-filled steel tube structure, the beam-column joint has a direct influence on the seismic performance of the overall structure, and therefore, the study on the seismic performance of the joint has great engineering application value. Some studies have been carried out on the seismic performance of concrete-filled steel tube column-beam joints. Wu et al. (2005,2007) conducted a study on a new concrete-filled steel tube column-beam bolted connection joint through low-cycle loading tests to investigate the seismic performance of joint. The results show that the bolted connection joint has good bearing capacity, deformation capacity, and energy dissipation capacity. Improper connections between prefabricated component joints can lead to serious damage and significant losses in prefabricated buildings. Therefore, the connections in prefabricated structures should have good load-bearing capacity, ductility, and energy dissipation capacity. Wu et al. (2020), Park et al. (2010) and Zhang et al. (2018) have investigated the seismic performance of the beam-column joints with different connections, including bolted connection, welded connection, and bolted-welded hybrid connection, through low-cycle loading tests. The results show that various beam-column connections have little effect on the ultimate failure modes of the beam-column joints, but the type of connection significantly affects on the seismic performance and load bearing capacity. Energy-dissipating bolts serve as a simple energy-dissipating device, connecting by bolts for easy assembly and disassembly, and plays the role of energy dissipation through plastic deformation after yielding under earthquake. Zhang and Li (2023) proposed a concrete-filled steel tube column-beam joint with energy dissipation bolts, and carried out low-cycle loading tests on the cross-shaped beam-column joints. The results of the loading test show that the hysteresis curves of the proposed beam-column joints are relatively complete, satisfying the requirement for high ductility and good energy dissipation capacity. The structure of the angle steel makes it have good load-bearing capacity. Under the same bearing strength, the weight of the angle steel is lighter, consuming less material and saving costs. Shafaei et al. (2014) and Tagawa and Liu (2014) proposed an RC beam-column joint with prestressed steel angles and conducted cyclic load experiments to study the seismic performance of this joint. The results showed that the strength, energy dissipation capacity, and ductility of the beam-column joint are significantly improved. In addition to the above-mentioned connection methods, the wide flange connection is widely used in beam-column joints due to its convenient material selection, resistance to deformation, and ease of maintenance. Gholami et al. (2013), Ricles et al. (2004) and Park et al. (2005) conducted experimental research on the concrete-filled steel tube column-steel beam joint with a wide flange, and analyzed the influence of the weld shape of the flange plate-flange fillet on the seismic performance. The results showed that the type of bolt hole in the beam-column joint had a significant effect on the overall seismic performance of the structure. A large number of results indicate that the type of bolt hole in column-beam connections has a significant impact on the overall seismic performance of the structure. Zhang et al. (2019a) proposed a new type of short shear link with shear slotted bolt connection and analyzed the hysteretic characteristics, damage modes, and energy dissipation mechanism of the link. The results showed that the deformation of the new short shear link is significantly lower than that of the conventional short shear link. Moreover, Ma et al. (2009) utilized finite element software to study the ductility deformation capacity, hysteresis performance, and energy dissipation capacity of the concrete-filled steel tube column-beam joint with elliptical holes and high-strength bolted connections. The results showed that the joint with elliptical bolt holes has good ductility and seismic performance. The aforementioned studies mainly focused on investigating the influence of connection types, bolt types, and hole shapes on the failure modes, ductility deformation capacity, hysteresis performance, and seismic performance of the concrete-filled steel tube column-beam joints. This could provide effective references for proposing a new type of joint and studying the seismic performance in this article.

Special-shaped columns refer to columns with L-shaped, T-shaped, or cross-shaped sections, where the thicknesses of the column limbs and adjacent walls are equal. Compared to traditional columns, special-shaped columns can improve the utilization rate of interior space and offer more building functionality, as well as better development prospects. Yang et al. (2022), Zhang et al. (2010), and Zhang et al. (2019b) conducted quasi-static tests on a planar frame with special-shaped concrete-filled steel tube columns and H-shaped steel beams. The results showed that as the axial compression ratio increased, the energy dissipation capacity and bearing capacity of the joints increased. Due to the fact that the cross-sectional width of T-shaped concrete-filled steel tube columns can be designed to be equal to that of the infill walls, the T-shaped concrete-filled steel tubular column-beam joint is a perfect solution to address the protruding wall issue of steel pipe concrete columns. Du et al. (2012) and Dong et al. (2023) conducted seismic performance tests on T-shaped concrete-filled steel tube columns-steel beams. The results showed that increasing the width and length of the side plates and ribbed plates significantly improved the ductility and energy dissipation capacity of the joints. The use of T-shaped stiffeners on the web of a beam can significantly improve the seismic performance of the beam-column joint, and is easy to process, manufacture, and install. Esfandyary et al. (2015), Cai et al. (2022), and Yang et al. (2020) studied the influence of internal and external stiffening ribs on the hysteretic behavior of concrete-filled steel tube columns and H-shaped steel beams. The results showed that the T-shaped stiffening ribs could improve the hysteresis behavior of the joints. The special-shaped steel tube concrete column-steel beam side plate connection has a simple structure, clear force transfer form, and convenient construction. Zhao et al. (2022a, 2022b, 2021) conducted quasi-static loading tests on a novel special-shaped concrete-filled steel tube column-beam joint with side plates. The results showed that by setting the side plates, plastic hinges could appear on the beams, meeting the seismic design requirements for building structures. Welding vertical ribs onto the specimen can delay the local buckling of the special-shaped tube and achieve the goal of improving the seismic performance of special-shaped tube concrete columns. Liu et al. (2017), Chen et al. (2021), and Bian et al. (2020) conducted experimental research and numerical analysis on the seismic performance of special-shaped concrete-filled steel tube column-beam joints. The results showed that the failure mode of the joint with vertical ribs was concrete tensile failure in the joint area, and it was recommended to set vertical ribs through the joint area to enhance its seismic performance. Due to the difficulty in repairing the damage caused by earthquakes to building structures, research on the restorability of steel structures after earthquakes is becoming a hot topic (Fang et al., 2022). Zhang et al. (2017) and Guo et al. (2016a,2016b) proposed a new design theory for corrugated web structures and verified the new theory. The results show that the components designed by the new theory can meet the needs of practical engineering, and the components have high seismic performance after rapid recovery after the earthquake. The concept of rapidly replacing joints with web openings after an earthquake was proposed. Jiang et al. (2022) conducted tests on beam-column joints with web openings, and the results showed that the joints with web openings had good seismic performance and post-earthquake repair ability. Wang et al. (2012) conducted low-cycle loading tests on six concrete-filled steel tube column H-shaped beam joints, and study the influence of flange and web openings on the failure mode of the joints. The test results showed that reasonable beam flange and web openings significantly alleviated the stress concentration on the beam flange. Hao et al. (2018) investigated the influence of hole size and location on the seismic performance of H-shaped steel beam joints with flange openings. For the concrete-filled steel tubular column-steel beam bolted connection, the size and arrangement of bolt holes directly affect the seismic performance and post-earthquake recovery speed of the components. Chen et al. (2015) carried out experiments and numerical analysis to investigate the influence of various bolt arrangements in the web on the seismic performance of column-beam joints. The results showed that when four bolts were arranged in a row, tearing failure occurred at bolt holes closer to the weld on the web. When the bolts were arranged in two rows, the web cracked at the bolt holes. The aforementioned studies mainly investigated the influence of bolt hole location, hole size, and various reinforcement structures, such as outer ring plates, side plates, and steel angles on the energy dissipation capacity and ductility of column-steel beam joints. This can provide a reference for the design of the spliced connection position and construction of the joint in this paper.

The column-beam joint is crucial in determining the internal force transmission within the components and the overall seismic performance of the structure. The complex stress conditions lead to difficulties in designing the column-beam joint, which is currently the main focus of research. Investigating the connection approach and seismic performance of the concrete-filled steel tube column-beam joint is of great significance in the engineering application of joints. Therefore, in order to significantly improve the seismic resistance and ductile rotation capacity of the joint without the need to increase additional consumables or significantly weakening the beam flanges, based on the widely used joint with an outer ring plate, this article proposes a new type of special-shaped concrete-filled steel tube column-beam joint. The column is welded to the cantilever beam section to move the plastic hinge outward and protect the beam-column welding joint. The cantilever beam section and the spliced beam section are bolted together. In the proposed joint, the beam and column are connected using bolt connections. To enhance the energy dissipation capacity of the joint, elliptical bolt holes are utilized to exert pressure on the bolts and the walls of the bolt holes. According to a series of finite element analyses, the seismic performance of the joint with different parameters are analyzed, including the form and size of the flange openings, the form and size of the web opening, and the thickness of the flange spliced plate. The influences of these parameters are investigated, which can provide a theoretical basis and reference for engineering design.

Overview of the test

Test parameters

In the experiment of literature (Liu, 2016), the specimen was a 1/2 scale model, with the beam length of 1.3 m and the column height of 1.65 m. The section of the steel beam was 100 mm × 7 mm × 200 mm × 4 mm, and the section of the column was a special-shaped column with a limb width of 100 mm. The width of the outer ring plate and the height of the vertical rib plate were taken as 75 mm and 50 mm, respectively. The specific parameters are shown in Figure 1.

Loading system

The loading system for the hysteresis test is proposed to adopt the principle of first load control first and then displacement control. The specific loading method is shown in Figure 2.

Typical failure mode of joint

The typical failure mode of the joint is shown in Figure 3. As shown in the figure, when the positive load is 43.5 kN, the specimen yielded in the positive direction, and the displacement is 28.3 mm. Then the horizontal displacement is applied, and when the displacement is positive 40 mm, the steel plate at the lower end of the joint buckles. When the displacement reached −80 mm, the steel plate in the joint region forms a cross buckle, causing the connection between the steel plate at the column end and the ring plate tears, leading to the failure of the component.

Verification of finite element analysis for seismic performance

Finite element model of a cross-shaped steel tube concrete column-beam joint

The finite element analysis software ABAQUS is used to establish the finite element (FE) model of the cross-shaped steel tube concrete column-I-beam joint as described in reference (Liu J, 2016) and to perform FE analyses. The FE models of the cross-shaped steel tube concrete column-I-beam frame joints under two different loading modes are shown in Figure 4. The steel tubes, concrete, steel beams, outer ring plates, and cover plates in the cross-shaped joints are modeled using a three-dimensional eight-node solid element C3D8R, while the reinforcement is modeled using a truss element T3D2. The interaction between the steel tube and steel beam, steel beams and outer ring plates, and cover plates and irregular steel pipe concrete is modeled using the tie constraint. The tension reinforcement is embedded throughout the entire structure. The cross-shaped steel pipes and core concrete are modeled using surface-to-surface contact, with the sliding formula being finite sliding. The normal behavior is set as hard contact, which allows for separation after contact. A penalty function with a friction coefficient of 0.6 is adopted as the formula for tangential friction behavior. In the contact interaction, it is specified that the joints on the surface cannot penetrate the main surface, but they can be penetrated by the nodes on the main surface. In addition to the binding constraints and contact interactions mentioned above, there are also coupling constraints in steel. After creating reference points at the beam ends and column ends, coupling constraints are added between the reference points and the ends of the beam and column, and then loads and constraint boundary conditions are applied. The bilinear constitutive model shown in Figure 5 is adopted for steel, while the plastic damage constitutive model shown in Figure 6 is adopted for concrete. The equivalent constitutive model of the restrained core concrete proposed by Liu W (2005) has been chosen, and the remaining plastic damage parameters for concrete are selected as shown in Table 1. The Poisson’s ratio of the core concrete is 0.2, and the elastic modulus is taken as $E_{c} = 4730 \sqrt{f_{c}} (N / m m^{2})$ ,where $f_{c}$ represents the axial compressive strength of the concrete.

Table 1.

The plastic damage parameters for concrete.

Expansion angle	Eccentricity	$f_{bo} / f_{c 0}$	K	Viscous parameter (E)
30°	0.1	44.2	0.66667	5-4

The boundary conditions for the column-end loading method can be seen in Figure 4(a). Symbols U1, U2, and U3 represent translational movement in three directions, while UR1, UR2, and UR3 represent rotation in three directions, respectively. The two ends of the column are hinged, and both the out-of-plane rotation and translational movement at the top of the column are constrained. Therefore, U2 = 0 and UR1 = UR3 = 0. At the bottom of the column, the three-dimensional translational movement and out-of-plane rotation are constrained. Therefore, U1 = U2 = U3 = 0 and UR1 = UR3 = 0. The beam end is hinged, and the three-dimensional translational movement and out-of-plane rotation are constrained, thus, U2 = U3 = 0 and UR1 = UR3 = 0. Based on the loading method described in the literature (Liu J, 2016), a constant axial pressure of 1342 kN (with an axial pressure ratio of 0.5) is applied to the top of the column. Afterward a horizontal load is applied. In this article, the displacement control mode is adopted for the horizontal load with an increment level of 5 mm. The loading process is shown in Figure 7.

The boundary conditions for the beam-end loading model are shown in Figure 4(b). For the top of the column, only vertical translational movement and in-plane rotation are allowed. Therefore, U1 = U2 = 0 and UR1 = UR3 = 0. The three-dimensional translational movement and out-of-plane rotation at the bottom of the column are constrained. Therefore, U1 = U2 = U3 = 0 and UR1 = UR3 = 0. For the beam end, out-of-plane translational movement and rotation are constrained. Therefore, U2 = 0 and UR1 = UR3 = 0. Based on the loading process presented in reference (Liao, 2019), the displacement control mode is used for the beam-end loading model. In this mode, the inter-story drift ratio is employed to control the loading step, as shown in Table 2.

Table 2.

Loading process for the beam-end loading model.

Loading level	Story drift angle (rad)	Beam-end loading displacement (mm)	Number of iterations
1	0.00375	5	1
2	0.005	7	1
3	0.0075	10	1
4	0.01	14.5	1
5	0.015	22	2
6	0.02	29	2
7	0.03	43.5	2
8	0.04	58	2
9	0.05	72.5	2
10	0.06	87	2
11	0.07	101.5	2

Finite element analysis results

The failure modes obtained from experimental and FE analyses are shown in Figure 8. In this figure, the degree of plastic damage ranges from 0 to 1, indicating the transition of the specimen from an intact state to a fully damaged state. It can be seen from the figure that the stress concentration in the core area of the joint results in a cross-buckling failure of the steel plates in the joint. The failure mode observed in the experiment, just like Figure 3, is consistent with that of the numerical simulation.

The hysteresis curves for the cross-shaped joint are compared in Figure 9. It can be seen from the figure that the hysteresis curve obtained by the column-end load method exhibits the same overall trend as the corresponding experimental hysteresis curve. However, the load-bearing capacity of the hysteresis curve obtained by finite element analysis is slightly lower than that obtained by experiment because the friction forces between the column hinge and the beam hinge have not been taken into account. For the beam-end loading method, the stiffness of the hysteresis curve obtained by finite element analysis is lower than that obtained by experiment due to the different transfer paths of the force, as well as the different materials and section sizes of the beam. In addition, the load-bearing capacity obtained by the beam-end loading method has been increasing.

The load and displacement of each characteristic point obtained from the experiment and finite element analyses are shown in Table 3. It can be seen from the table that the yield displacement, peak displacement, and ultimate displacement obtained by the experiments and finite element analyses are 8.7%, 8.5%, and 4.2% different, respectively. The yield load, peak load, and ultimate load are 7.9%, 8.3%, and 7.7% different, respectively. The errors of the load-bearing capacity and displacement of the finite element analyses compared to the experiment results are within 10%, indicating that the finite element analysis can actually reflect the experimental process. For the beam-end loading method, the load-bearing capacity differs by 15.9% from the experimental results, and differs by 8.4% from the column-end loading method. The ultimate displacement angle of the column-end loading method is similar to that of the beam-end loading method, suggesting that the finite element analyses using these two different loading methods are effective. However, this article mainly focuses on the plastic hinge region of the beam end and joint core. Therefore, the following studies of seismic performance of the joints are conducted based on the beam-end loading method.

Table 3.

Comparison of the feature points in the hysteresis curves.

	Yield displacement (mm)		Yield load (kN)		Peak displacement (mm)		Peak load (kN)		Damage displacement (mm)		Damage load (kN)
Loading direction	+	-	+	-	+	-	+	-	+	-	+	-
Experiment	25.31	21.37	62.22	65.73	37.73	33.52	72.64	74.28	55.46	52.21	61.04	63.14
Column-end loading	21.97	20.47	59.66	58.07	34.94	30.29	67.29	67.50	52.34	53.67	57.20	57.40
Beam-end loading	27.83	27.95	50.42	51.51	101.14	98.50	62.72	60.78

General situation of novel steel tube special-shaped column-beam joint

Considering different methods of improving joints, strengthening the joint will cause the plastic hinge to move away from the column. On the other hand, weakening the joint will decrease the load-bearing capacity of the joint due to the weakened region near the joint. To overcome the limitations of the aforementioned methods for improvement, this paper proposes a new approach to enhance the joint by setting elliptical holes in the beam flanges. This new joint can greatly improve the energy dissipation and ductile rotation capabilities of the joint without requiring additional parts and significantly weakening the beam flanges.

Dimension of the novel special-shaped concrete-filled steel tube column-beam joint

Figure 10 shows a detailed diagram of a 1/2 scale model of the proposed special-shaped steel tube column beam joint. The column has a height of 1650 mm and a cross-shaped limb width of 100 mm. The beam has a length of 1300 mm and an I-section size of 100 mm × 7.37 mm × 200 mm × 4.44 mm. The outer ring plate has a width of 75 mm. The diameter of the reinforcement bars is 6 mm, and the vertical spacing between the reinforcement bars in the column is 100 mm. The high-strength bolts and connecting plates are spliced together at the joint in the connection part. The size of the connecting plate outside and inside the flange is 6 mm $\times$ 100 mm $\times$ 310 mm and 6 mm $\times$ 42 mm $\times$ 310 mm, respectively. The size of the connecting plate on the web is 4 mm $\times$ 220 mm $\times$ 150 mm. The beam flange and web plate were spliced using high-strength bolts with diameters of 12 mm.

Parameters for seismic performance analyses

In this article, a series finite element analyses are carried out to investigate the seismic performance of the joints. The bolt-hole shape of the flange and web, hole size on the flange and web, thickness of spliced plate of flange and axial compression ratio are selected as the main design parameters, and a total of 12 joints with different parameters are considered, as shown in Table 4. When determining the size of the elliptical hole, refer to the Chinese Code for seismic design of buildings (GB 50011-2010, 2010) and Code for design of steel structures (GB 50017-2017, 2017), the size of the elliptical hole is determined according to equation (1). The calculation results are shown in Table 5.

r_{1} = h \times θ_{2} + r

(1)

where r₁ is the radius of the long axis opening, r is the bolt radius, and θ₂ is the slip angle of the splicing.

Table 4.

Parameters for seismic performance analyses of joints.

Specimennumber	Flange aperture (mm × mm)	Web aperture (mm × mm)	Thickness of wing spliced slabs (mm)	Compression ratio	Joint type
G-01	-	-	-	0.5	Modification of spliced beam type
G-02	13.5 × 13.5 (Circular holes)	13.5 × 13.5 (Circular holes)	6	0.5	Modification of spliced beam type
G-03	13.5 × 15.5 (Elliptical holes)	13.5 × 13.5 (Circular holes)	6	0.5	Flange flaring type
G-04	13.5 × 16.5 (Elliptical holes)	13.5 × 13.5 (Circular holes)	6	0.5
G-05	13.5 × 17.5 (Elliptical holes)	13.5 × 13.5 (Circular holes)	6	0.5
G-06	13.5 × 18.5 (Elliptical holes)	13.5 × 13.5 (Circular holes)	6	0.5
G-07	13.5 × 16.5 (Elliptical holes)	13.5 × 15.5 (Elliptical holes)	6	0.5	Web reaming type
G-08	13.5 × 16.5 (Elliptical holes)	13.5 × 16.5 (Elliptical holes)	6	0.5
G-09	13.5 × 16.5 (Elliptical holes)	13.5 × 17.5 (Elliptical holes)	6	0.5
G-10	13.5 × 16.5 (Elliptical holes)	13.5 × 13.5 (Circular holes)	4	0.5	Cover plate thickness change type
G-11	13.5 × 16.5 (Elliptical holes)	13.5 × 13.5 (Circular holes)	7.37	0.5
G-12	13.5 × 16.5 (Elliptical holes)	13.5 × 13.5 (Circular holes)	8	0.5

Table 5.

Calculation results of ellipse hole size.

Joint parameters	JD1	JD2	JD3	JD4	JD5
Slip angle θ₂	0	0.01	0.02	0.03	0.04
Ellipse hole size mm × mm	13.5 × 13.5	13.5 × 15.5	13.5 × 16.5	13.5 × 17.5	13.5 × 18.5

Finite element analysis of the seismic behavior of the special-shaped steel tube concrete column-beam joint

Finite element model of joint

The finite element model for the proposed special-shaped concrete-filled steel tube column-beam joint is shown in Figure 11. The main modeling methods in this model are the same as those introduced in Section 2.1. Considering the contact between different components, the surface-to-surface contact is adopted for the bolt caps and connection plates, as well as for connection plates and beams. The formula used for this contact is finite sliding. The normal behavior is set as hard contact, which allows separation after contact. A penalty function with a friction coefficient of 0.45 is adopted to represent tangential friction behavior, and the friction coefficient between the bolt rod and bolt holes is set as 0.3. The load and boundary conditions are the same as the beam-end loading method introduced in Section 2, and the pretension forces of the bolts are set as 55 kN.

Seismic performance analysis

Failed modes

The stress contour of specimens G-01 and G-02 in their ultimate state are shown in Figure 12. In the initial loading stage, the stresses in the joint core and the spliced region of the two specimens began to increase, and a small concentrated stress occurs at the end of the beam. As the displacement load increases, the stresses in the joint core and spliced region continue to increase and spread outward, causing the steel tube column and beam end to yielding. In the later stage of loading, the stress concentration occurs in the joint core, beam-column connection region, and beam flange close to the column end for specimen G-01. While for specimen G-02, the stress concentration occurs in the joint core, spliced region, region around the bolts in the middle of the spliced plate, and the portion of the beam near to the spliced plate.

Hysteresis curve

Figure 13 shows the hysteresis curves of specimens G-01 and G-02. It can be observed that the overall trend and hysteresis loop area of the hysteresis curve for specimen G-01 are essentially identical to those of specimen G-02. At the initial stage of loading, the hysteresis curves of the two specimens are almost linear. As the displacement load increases, the hysteresis loop becomes complete. The overall shapes of the hysteresis curves are basically symmetrical, and the transition is smooth. The results indicate that the equal-strength splicing design method for the joints in the article is relatively valid and accurate. Due to the bolt connection in the spliced region of specimen G-02, the stiffness is slightly higher, resulting in a slightly greater bearing capacity than specimen G-01 with non-spliced beam. The ultimate load carrying capacities of G-01 and G-02 are 62.72 kN and 65.16 kN, respectively. The bearing capacity of the spliced beam specimen is 3.9% higher than that of the non-spliced beam specimen, indicating that the utilization of bolts increases the stiffness of the spliced region, and therefore results in a higher bearing capacity of the spliced beam.

Ductility factor

The displacement ductility factors of the specimens are shown in Table 6. It can be seen that the displacement ductility factor of G-02 is lower than that of G-01. The reason for this is that the use of the equal-strength design method could increase the stiffness of the spliced beam, and result in a weaker ductility deformation capacity of the joint.

Table 6.

Displacement ductility coefficients of specimens G-01 and G-02.

Specimen	Ultimate displacement $Δ_{u} (mm)$	Yield displacement $Δ_{y} (mm)$	Displacement ductility coefficients μ
G-01	99.82	27.89	3.58
G-02	99.55	29.81	3.34

Energy dissipation capacity

In this article, the equivalent viscous damping coefficient $ζ$ is used to represent the energy dissipation capacity of the joint. The calculation diagram for the equivalent viscous damping coefficient $ζ$ is shown in Figure 14, and $ζ$ can be calculated according to equation (2).

ζ = \frac{1}{2 π} \times \frac{S_{A B C} + S_{C D A}}{S_{O B E} + S_{O D F}}

(2)

where

S_{A B C}

and

S_{C D A}

represent the shaded areas of the hysteresis loop,

S_{O B E}

and

S_{O D F}

are the areas of triangles OBE and ODF, respectively.

According to equation (11), the equivalent viscous damping coefficients for G-01 and G-02 can be calculated, as shown in Table 7.

Table 7.

The equivalent viscous damping coefficients for G-01 and G-02.

Specimens	0.02 rad	0.03 rad	0.04 rad	0.05 rad	0.06 rad	0.07 rad
G-01	0.393	0.504	0.547	0.561	0.550	0.550
G-02	0.383	0.474	0.531	0.517	0.501	0.501

It can be seen from the table that the maximum equivalent viscous damping coefficients of G-01 and G-02 are 0.561 and 0.531, respectively, with a difference of 5.3%. This indicates that the joint with a spliced beam designed by the equal-strength design method could result in a lack of ductility deformation capacity in the spliced region and reduce the energy dissipation capacity.

Seismic performance analysis of beam-column joints with various flange holes

Failed modes

The stress contour of specimens G-02∼G-06 with various flange openings in the ultimate state are shown in Figure 15. Taking specimen G-04 as an example, when the loading displacement angle is 0.01 rad, the stress in the joint core and spliced beam section area increases, and a small concentrated stress occurs at the end of the beam. When the loading displacement angle reaches 0.03 rad, the stress in the column and beam end continues to increase, and the stress in the spliced plate and beam flange under the spliced plate begins to increase. When the loading displacement angle reaches 0.05 rad, the stress in the area near the third row of the bolt holes in the spliced plate begins to spread to the area near the fourth row of the bolt holes, and the yield area in the beam end increases. When the loading displacement angle reaches 0.07 rad, the stress in the spliced region begins to spread to both ends, and the yield area increases. Additionally, as the size of the flange opening hole increases, the stress in the beam-column joint gradually decreases. However, the stress in the web bolt hole and the surrounding area of the beam increases, indicating that the elliptical holes in flange can cause the plastic hinge to move outward from the connection of the beam-column joint to the beam web.

Hysteresis curve

The loading-displacement hysteresis curves of specimens G-02 to G-06 are shown in Figure 16. It can be observed that the overall shape of the hysteresis curve of G-02 is essentially symmetrical, and the hysteresis loop is complete. For specimens G-03 to G-06, when the displacement reaches 43.5 mm, the hysteresis curves begin to show a parallelogram shape, indicating an improvement in plastic deformation capabilities. The hysteresis loop areas are larger than those of G-02, indicating that the flange opening could increase the energy dissipation capacity of the joints. The ultimate bearing capacities of specimens G-03 to G-06 are 64.38 kN, 63.85 kN, 62.77 kN, and 61.21 kN, respectively. The values are is 1.2%, 2%, 3.7%, and 6.1% lower than that of specimen G-02, indicating that the elliptical holes in flange can slightly reduce the bearing capacity of the specimen.

Ductility factor

The displacement ductility factors of specimens G-02 to G-06 are shown in Table 8. It can be seen that the displacement ductility factor of specimen G-02 is the smallest, with a value of 3.34. The displacement ductility factors of G-03 to G-06 increase as the size of the opening hole increases. The factor increased by 5.4%, 8.1%, 8.4%, and 9%, respectively. This means that as the size of the opening hole increases, the ductility deformation capacity of the joint also increases, indicating that elliptical holes in the beam flange can significantly enhance the ductility deformation capacity of the joints.

Table 8.

The displacement ductility factors of specimens G-02 to G-06.

Specimens	Ultimate displacement $Δ_{u} (mm)$	Yield displacement $Δ_{y} (mm)$	Displacement ductility coefficients μ
G-02	99.55	29.81	3.34
G-03	100.90	28.65	3.52
G-04	101.30	28.08	3.61
G-05	100.56	27.77	3.62
G-06	100.58	27.64	3.64

Energy dissipation capacity

The maximum equivalent viscous damping coefficients of specimens G-02 to G-06 are shown in Table 9. It can be seen from the table that compared to specimen G-02, the maximum equivalent viscous damping coefficients of the flange opening joints G-03 to G-06 increased by 2.3%, 7.2%, 10.7%, and 15.3%, respectively, indicating that the energy dissipation capacities of the joints are significantly improved by opening elliptic holes in the beam flanges.

Table 9.

The equivalent viscous damping coefficients for G-02 to G-06.

Specimen	0.02 rad	0.03 rad	0.04 rad	0.05 rad	0.06 rad	0.07 rad
G-02	0.383	0.474	0.531	0.517	0.501	0.501
G-03	0.388	0.520	0.543	0.522	0.502	0.502
G-04	0.401	0.538	0.569	0.543	0.514	0.502
G-05	0.409	0.558	0.588	0.574	0.527	0.503
G-06	0.413	0.571	0.605	0.612	0.550	0.508

Seismic performance analysis of beam-column joints with various web holes

Failed modes

The stress contour of the ultimate states of specimens G-04, G-07, G-08, and G-09 are shown in Figure 17. It can be observed that the failure process and failure modes of the four specimens are essentially consistent, suggesting that the enlargement of the web opening hole has little effect on the stress in the beam-column joint.

Hysteresis curve

The load-displacement hysteresis curves for the beam ends of the specimens with various web opening holes are shown in Figure 18. It can be seen that as the displacement increases, the shapes of the hysteresis curves for the four specimens are essentially identical. The ultimate bearing capacities of G-04, G-07, G-08, and G-09 are 63.85 kN, 63.57 kN, 63.93 kN, 63.51 kN, respectively, indicating that expanding the bolt holes in the web has less effect on the hysteretic performance of the joints.

Ductility factor

The displacement ductility coefficients of the specimens with various web holes are shown in Table 10. It can be seen that the maximum difference in the displacement ductility coefficients of the four specimens is less than 2%, indicating that enlarge the bolt holes in the web has a less effect on the ductility deformation capacity of the joints.

Table 10.

The displacement ductility coefficients of the specimens with various web holes.

Specimens	Ultimate displacement $Δ_{u} (mm)$	Yield displacement $Δ_{y} (mm)$	Displacement ductility coefficient μ
G-04	101.30	28.08	3.61
G-07	99.67	28.19	3.54
G-08	99.59	27.77	3.59
G-09	100.24	28.06	3.57

Energy dissipation capacity

The maximum equivalent viscous damping coefficients of the joints with various web holes are shown in Table 11. It can be seen that the maximum difference among the maximum equivalent viscous damping coefficients of specimens G-04, G-07, G-08, and G-09 is 1.4%, indicating that enlarging the bolt holes in the web has little effect on the energy dissipation capacity of the joints.

Table 11.

The equivalent viscous damping coefficients of the specimens with various web holes.

Specimens	0.02 rad	0.03 rad	0.04 rad	0.05 rad	0.06 rad	0.07 rad
G-04	0.401	0.538	0.569	0.543	0.514	0.502
G-07	0.406	0.547	0.571	0.550	0.514	0.497
G-08	0.410	0.548	0.577	0.549	0.508	0.498
G-09	0.419	0.551	0.577	0.549	0.514	0.498

Seismic performance analysis of beam-column joints with various thickness of spliced plates

Failed modes

The stress contour of the specimens G-04, G-10, G-11, and G-12 in their ultimate state are shown in Figure 19. It can be seen that the failure modes and stress distributions of G-04, G-11, and G-12 are essentially identical. In the later stage of loading, the failure modes were all yielding in the beam end, the region around the bolt holes outside of the spliced region, and the region around the bolt holes on the web plate. However, specimen G-10 which has a 4 mm thickness of spliced plate exhibits an extrusion failure mode during the later stage of loading because the spliced plate is too thin, and the stress concentration occurs at the spliced region. The results indicate that the thickness of the spliced plate ranging from 6 mm to 8 mm, has a little effect on the seismic performance of the joint, while if the spliced plate is too thin, the seismic performance can be decreased.

Hysteresis curve

The load-displacement hysteresis curves for specimens with various thicknesses of spliced plates are shown in Figure 20. It can be seen that as the displacement load increases, the hysteresis curves for the joints with spliced plates of thickness 6 mm, 7.37 mm, and 8 mm exhibit the same trend, and the bearing capacities gradually increase. However, for specimen G-10 with a 4 mm thickness of spliced plate, the bearing capacity significantly decreases when the loading displacement at the beam end is 57 mm, and the hysteresis curve is interrupted after a negative loading displacement of 85 mm. This is because the spliced plate is too thin, and the spliced plate is damaged during the loading process, indicating that the thickness of the spliced plate should be selected within a reasonable range to prevent damage.

Ductility factor

The displacement ductility factors of the specimens with various thicknesses of the spliced plate are shown in Table 12. It can be seen that the displacement ductility factors of specimens G-04, G-10, G-11, and G-12 are 3.61, 4.94, 3.51, and 3.44, respectively. Compared to G-10 with a 4 mm thickness of spliced plate, the displacement ductility factors of specimens G-04, G-11, and G-12 decrease by 26.9%, 28.9%, and 30.4%, respectively.

Table 12.

The displacement ductility factors by various thicknesses of the spliced plate.

Specimens	Ultimate displacement $Δ_{u} (mm)$	Yield displacement $Δ_{y} (mm)$	Displacement ductility coefficients μ
G-04	101.30	28.08	3.61
G-10	86.06	17.42	4.94
G-11	99.23	28.29	3.51
G-12	98.17	28.56	3.44

Energy dissipation capacity

The maximum equivalent viscous damping coefficients of joints with various thicknesses of spliced plates are shown in Table 13. From the table, it can be seen that the thicknesses of the spliced plates for specimens G-04, G-11, and G-12 are 6 mm, 7.37 mm, and 8 mm, respectively. The maximum equivalent viscous damping coefficients of them are 0.569, 0.568, and 0.568, which are very close to each other. For specimen G-10, the maximum equivalent viscous damping coefficient is 0.657. Compared to specimen G-10, the maximum equivalent viscous damping coefficients of specimens G-04, G-11, and G-12 decrease by 13.4%, 13.5%, and 13.5%, respectively, indicating that for joint design, it is not necessary to use a spliced plate that is too thick as long as the economic efficiency, seismic performance, and load bearing capacity are ensured.

Table 13.

The equivalent viscous damping coefficients by various thicknesses of the spliced plate.

Specimens	0.02 rad	0.03 rad	0.04 rad	0.05 rad	0.06 rad	0.07 rad
G-04	0.401	0.538	0.569	0.543	0.514	0.502
G-10	0.442	0.546	0.588	0.657	0.631
G-11	0.365	0.523	0.541	0.568	0.532	0.521
G-12	0.356	0.496	0.568	0.567	0.546	0.531

Design method for novel steel tube special-shaped column-beam joint

Based on the above numerical simulation results and relevant Chinese codes (Xing R et al., 2014; JGJ99—2015, 2015), the joint is designed according to the principle of equal strength, and the bearing capacity can be designed as shown below.

Calculation of spliced connection

(1) Bearing capacity of the friction high-strength bolt:

The shear bearing capacity of a single friction-type high-strength bolt can be calculated according to equation (3):

N_{v}^{b} = k_{1} k_{2} n_{f} P_{μ}

(3)

where

k_{1}

is the coefficient, which is taken as 0.8 for cold-formed thin-walled steel structures and 0.9 for other cases.

k_{2}

is the hole coefficient, which is taken as 1.0 for standard holes, 0.85 for large circular holes, 0.7 when the load is perpendicular to the direction of the slot, and 0.6 when the load is parallel to the long direction of the slot.

n_{f}

is the number of friction surfaces,

P

is the pre-tension of each high-strength bolt, and

μ

is the anti-slip coefficient.

(2) Estimation of the number of connecting bolts:

The number of high-strength bolts on one side of the weakened beam flange can be calculated according to equation (4):

n_{F b} = \frac{A_{n F} f}{N_{V}^{b}}

(4)

The number of high-strength bolts on the weakened beam web can be calculated according to equation (5):

n_{W b} = \frac{A_{n W} f_{v}}{N_{V}^{b}}

(5)

where

f

is the design value of tensile, compressive and bending strength of steel, and

f = 215 N / {mm}^{2}

f_{v}

is the design value of shear strength of steel, and

f_{v} = 125 N / {mm}^{2}

A_{n F}

is the net section area of steel beam flange, and

A_{n W}

is the net section area of steel beam web.

Calculation of elastic design

The bending moment and shear force of the steel beam are designed according to equal strength, and the design satisfies equations (6) and (7) respectively:

M_{n}^{b} = W_{n}^{b} f

(6)

V_{n}^{b} = A_{n W} f_{v}

(7)

where

W_{n}^{b}

is the net section modulus of the steel beam considering bolt holes.

Ultimate bearing capacity calculation

The ultimate shear bearing capacity of a single bolt $N_{v u}^{b}$ can be calculated according to equation (8):

N_{v u}^{b} = 0.58 n_{f} A_{e}^{b} f_{u}^{b}

(8)

where

A_{e}^{b}

is the effective area of bolt thread.

The bearing capacity of flange $N_{c u}^{b}$ can be calculated according to equation (9):

N_{c u}^{b} = d \sum t f_{c u}^{b}

(9)

where

f_{c u}^{b}

is the ultimate bearing strength of the connection plate.

The bearing capacity of web $N_{c u}^{b}$ is can be calculated according to equation (10):

N_{c u}^{b} = d \sum t f_{c u}^{b}

(10)

Both the flange and web should meet the requirements:

N_{v u}^{b} ⩾ N_{c u}^{b}

(11)

Calculation of the connection between the steel tube concrete column and steel beam

(1) The bending capacity and shear capacity of the column-beam connection are calculated should meet the following equations:

M_{u} = A_{F} (H - t_{F b}) f_{u b} + M_{c} - \frac{V_{d}}{3} > 1.4 M_{p}

(12)

V_{u} = \frac{(H - 2 t_{F b}) t_{W b} f_{u b}}{\sqrt{3}} > 1.4 (\frac{2 M_{p}}{l_{n}})

(13)

where

A_{F}

t_{F b}

and

f_{u b}

are the gross sectional area, thickness and minimum tensile strength of the beam flange, respectively.

M_{c}

and

V_{d}

are the bending and shearing capacities of the column, respectively.

M_{p}

is the ultimate bending capacity of the spliced region of the beam, which is taken as 130.26

kN \cdot m

in this paper.

t_{W b}

is the thickness of the web,

H

is the section height of beam.

f_{a y}

is the yield strength of the spliced component,

f_{u}^{b}

is the minimum tensile strength of the bolt, which is taken as 1.5

f_{u}

f_{u}

is the minimum tensile strength of the component, and

l_{n}

is the net span of the beam.

Conclusion

Based on the above research, this article presents the following primary conclusions:

(1) A finite element model of the cruciform concrete-filled steel tubular column-I-beam joint was established using ABAQUS software. The load-displacement relationship of each characteristic point obtained by finite element analysis using the column-end loading method show a good agreement with the experimental results. The beam-end loading method is equivalent to the column-end loading method, and both methods can be used to analyze the seismic performance of the joint.

(2) Compared with the column-beam joint without spliced beams, the ultimate bearing capacity of the column-beam joint with the spliced beam increases by approximately 3.9%. Additionally, the maximum equivalent viscous damping coefficient decreases by 5.3% and the ductility coefficient decreases by 6.7%, respectively. The column joints, whether with or without spliced beams, exhibit similar seismic performance.

(3) According to the analysis results for the column-beam joints with varying bolt opening holes in the flange, it can be concluded that enlarging the holes in the flange will slightly decrease the bearing capacity of the joint. However, it will significantly improve the energy dissipation capacity and ductility deformation capacity of the joint. Therefore, it is suggested to use a joint with elliptical holes in the flange in practical engineering. In addition, the analysis results for the column-beam joints with varying bolt opening holes in the web show that the elliptical bolt holes in the web have little effect on the seismic performance of the joint.

(4) According to the analyses for the column-beam joints with varying thicknesses of spliced plates, it has been proven that the thickness of the spliced plate within a range of 6 mm to 8 mm has little effect on the seismic performance of the column-beam joints. The energy dissipation capacity of the joint with a 4 mm thick of the spliced plate significantly increases, but the spliced plate breaks during the loading process. Therefore, it is suggested that on the premise of ensuring economic efficiency, seismic performance, and load-bearing capacity, there is no need to use an excessively thick spliced plate.

Footnotes

Author contributions

Chunyang Liu: Conceptualization, Methodology, Software, Validation, Formal analysis, Data collation, Writing-manuscript, Writing-review and editing, Visualization.

Jihe Qin: Investigation, Data collection, Data interpretation, Writing-review and editing.

Zhenfan Gong: Data interpretation, Writing-review and editing.

Hao Wang: Methodology, Writing-review and editing.

Guangkai Zhou: Research, Methodology.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China under Grant no. 52278507, the Natural Science Foundation of Shandong Province under Grant no. ZR2022ME160.

ORCID iD

Hao Wang

Data availability statement

Data will be made available on request. *

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